In the present work, in order to circumvent the significant softening of the EOS in the case of the (\(Y\) +\(K\) ) phase, we take into account the repulsion by the UTBR.
We adopt the RMF model for two-body \(B\) -\(B\)  interaction mediated by meson-exchange, discarding the nonlinear self-interacting meson potentials [1]}. We call this model a minimal RMF (MRMF) throughout this paper. We introduce the density-dependent effective two-body potentials for the UTBR, which has been derived from the string-junction model by Tamagaki [2]} and originally applied to \(Y\) -mixed matter by Tamagaki, Takatsuka and Nishizaki[3]}. Together with the UTBR, phenomenological three-nucleon attraction (TNA) is taken into account, and we construct the baryon interaction model that reproduces saturation properties of symmetric nuclear matter (SNM) and empirical values of incompressibility, symmetry energy, and its slope at the nuclear saturation density \(\rho _0\)  (= 0.16 fm\(^{-3}\) ).
Then we consider the (\(Y\) +\(K\) ) phase based upon the effective chiral Lagrangian coupled with the present baryon interaction model (MRMF+UTBR+TNA). Effects of the UTBR and TNA on the whole EOS with the (\(Y\) +\(K\) ) phase are clarified.
As implications for thermal evolution of neutron stars, rapid cooling mechanisms in the presence of the (\(Y\) +\(K\) ) phase are briefly mentioned.
